Let AC be 2 units.
a = √(2²+2²)
a = √(8) units.
a = 2√(2) units.
Let the side length of the inscribed regular hexagon be b.
c² = 2b²-2b²cos120
c = √(3)b units.
d = 0.5b units.
e = √(2) units....
a² =10²-6²
a = 8 cm.
tanb = 3/4
b = atan(3/4)°
(3/4) = c/10
c = ½(15) cm.
c = 7.5 cm.
sin(atan(3/4)) = d/8
d = 4.8 cm.
e = 7.5-4.8
e = 2.7 cm.
(3/4) = 2.7/f
f = 3.6 cm.
g² = 2.7²+3.6²
g = 4.5...
Sir Mike Ambrose is the author of the question.
Let alpha be x.
tanx = 10/a --- (1)
tan2x = a/30 --- (2)
From (2)
a = 30tan2x --- (3)
Sub. (3) in (1)
tanx = 10/30tan2x
tanxtan2x = ⅓
tanx(2tanx/(1...
Let the three congruent semi circles radius be 2 units.
Calculating radius, r of the ascribed quarter circle.
Let it be a.
2b² = 2²
b = √(2) units.
4²-√(2)² = c
c = √(14) units.
It implies;
a...
Sir Mike Ambrose is the author of the question.
Let the side of the regular pentagon be 1 unit.
Area regular pentagon is;
½(5)*(1/(2tan(36)))
= 1.72047740059 square units.
a = ⅕(180*3)
a = 108°
(1...
Let the side length of the regular hexagon be 1 unit.
a² = 2-2cos120
a = √(3) units.
Notice;
AB = AC
Calculating y.
It implies;
((√(3)-1)/sin75) = (y/sin45)
y = (4-2√(3)) units.
x = 1-y
x = 1...
Sir Mike Ambrose is the author of the question.
Notice;
BC = 2 units.
a = ⅛(180*6)
a = 135°
b = 2+2(2sin45)
b = 4.82842712475 units.
c = b+2
c = 6.82842712475 units.
Let AB be d.
Calculating d....
Let the regular pentagon side be 1 unit.
Let the width and length of the inscribed red rectangle be a and b respectively.
(1/sin72) = (c/sin54)
c = 0.85065080835 units.
d = 180-54-108
d = 18°
(d...
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Sir Mike Ambrose is the author of the question.
tan30 = 1/a
a = √(3) units.
b = a-1
b = (√(3)-1) unit.
It implies;
Area Shaded in square units exactly as a single fraction is;
Area triangle with...
